Liquidation cost.
Following the framework of [1]}, we define the cost process (or loss process) \(C^{x,\pi } \triangleq (C_t^{x,\pi })_{t \ge 0}\)  as
\( C_t^{x,\pi } \triangleq \int _{s=0}^t \frac{1}{2} \eta \pi _s^2 ds - \int _{s=0}^t \sigma X_s^{x,\pi } dW_s.\) 
